共查询到20条相似文献,搜索用时 31 毫秒
1.
Asymmetric variational inequality problems over product sets: Applications and iterative methods 总被引:5,自引:0,他引:5
Jong-Shi Pang 《Mathematical Programming》1985,31(2):206-219
In this paper, we (i) describe how several equilibrium problems can be uniformly modelled by a finite-dimensional asymmetric
variational inequality defined over a Cartesian product of sets, and (ii) investigate the local and global convergence of
various iterative methods for solving such a variational inequality problem. Because of the special Cartesian product structure,
these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality
subproblems in lower dimensions. The resulting decomposition schemes often have a natural interpretation as some adjustment
processes.
This research was based on work supported by the National Science Foundation under grant ECS 811–4571. 相似文献
2.
In this work, the contact problem between an elastic body and a rigid obstacle is studied, including the development of material damage which results from internal compression or tension. The variational problem is formulated as a first-kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field. The existence of a unique local weak solution is stated. Then, a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived on the approximate solutions, from which the linear convergence of the algorithm is deduced under suitable regularity conditions. Finally, three two-dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme. 相似文献
3.
Iterative methods for variational and complementarity problems 总被引:12,自引:0,他引:12
In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.This research was based on work supported by the National Science Foundation under grant ECS-7926320. 相似文献
4.
1.IntroductionPartialdifferentialequationssubjecttounilateralboundaryconditionsareusuallycalledSignoriniproblemsintheliterature.TheseproblemshavebeenstudiedbymanyauthodssincetheappearenceofthehistoricalpaperbyA.Signoriniin1933[25].Signoriniproblemsaroseinmanyareasofapplicationse.g.,theelasticitywithunilateralconditions[lo],thefluidmechnicsproblemsinmediawithsemipermeableboundaries[8,12],theelectropaintprocess[1]etc.Fortheexistence,uniquenessandregularityresultsforSignorinitypeproblemswerefer… 相似文献
5.
为研究摩擦接触问题,本文建立了一个具有二类独立交量的二维弹塑性梁模型。由此提出了一个新的非线性二次互补性问题。其中的外部互补性条件定义了自由边界;而内部互补性条件则控制了弹塑性分界面。文中证明了此二次互补性问题等价于一非线性变分不等式,并导出了其对偶变分不等式。本文结果显示对偶问题较原问题有更多的优越性。应用于塑性极限分析理论中,文中最后证明了一个简单的下限定理。 相似文献
6.
We consider the numerical solution of a nonlinear evolutionary variational inequality, arising in the study of quasistatic contact problems. We study spatially semi-discrete and fully discrete schemes for the problem with several discontinuous Galerkin discretizations in space and finite difference discretization in time. Under appropriate regularity assumptions on the solution, a unified error analysis is established for the schemes, reaching the optimal convergence order for linear elements. Numerical results are presented on a two dimensional test problem to illustrate numerical convergence orders. 相似文献
7.
Global Method for Monotone Variational Inequality Problems with Inequality Constraints 总被引:2,自引:0,他引:2
J. M. Peng 《Journal of Optimization Theory and Applications》1997,95(2):419-430
We consider optimization methods for monotone variational inequality problems with nonlinear inequality constraints. First, we study the mixed complementarity problem based on the original problem. Then, a merit function for the mixed complementarity problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original variational inequality problem is reformulated as simple bounded minimization. Under certain assumptions, we show that any stationary point of the optimization problem is a solution of the problem considered. Finally, we propose a descent method for the variational inequality problem and prove its global convergence. 相似文献
8.
The Zeno phenomenon of a switched dynamical system refers to the infinite number of mode switches in finite time. The absence
of this phenomenon is crucial to the numerical simulation of such a system by time-stepping methods and to the understanding
of the behavior of the system trajectory. Extending a previous result for a strongly regular differential variational inequality,
this paper establishes that a certain class of non-strongly regular differential variational inequalities is devoid of the
Zeno phenomenon. The proof involves many supplemental results that are of independent interest. Specialized to a frictional
contact problem with local compliance and polygonal friction laws, this non-Zenoness result is of fundamental significance
and the first of its kind.
This work was based on research partially supported by the National Science Foundation under grants DMS-0508986 and IIS-0413227
awarded to Rensselaer Polytechnic Institute, where the original version of the paper was first written. The revision was based
on research partially supported by the National Science Foundation under grant DMS awarded to the University of Illinois at
Urbana-Champaign. 相似文献
9.
Russell M. Brown Zhongwei Shen Peter Shi 《Transactions of the American Mathematical Society》1998,350(10):4053-4063
We consider a variational inequality for the Lamé system which models an elastic body in contact with a rigid foundation. We give conditions on the domain and the contact set which allow us to prove regularity of solutions to the variational inequality. In particular, we show that the gradient of the solution is a square integrable function on the boundary.
10.
M. Cocou 《Applicable analysis》2018,97(8):1357-1371
The aim of this paper is to study an evolution variational inequality that generalizes some contact problems with Coulomb friction in small deformation elasticity. Using an incremental procedure, appropriate estimates and convergence properties of the discrete solutions, the existence of a continuous solution is proved. This abstract result is applied to quasistatic contact problems with a local Coulomb friction law for nonlinear Hencky and also for linearly elastic materials. 相似文献
11.
Hybrid finite element methods for the Signorini problem 总被引:3,自引:0,他引:3
We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falk's Lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them. Two of these finite elements provide optimal results under reasonable regularity assumptions on the Signorini solution, and the numerical investigation shows that the third method also provides optimal accuracy.
12.
In this paper we are concerned with a kind of nonlinear transmission problem with Signorini contact conditions. This problem can be described by a coupled FEM-BEM variational inequality. We first develop a preconditioning gradient projection method for solving the variational inequality. Then we construct an effective domain decomposition preconditioner for the discrete system. The preconditioner makes the coupled inequality problem be decomposed into an equation problem and a “small” inequality problem, which can be solved in parallel. We give a complete analysis to the convergence speed of this iterative method. 相似文献
13.
David Kinderlehrer 《Applied Mathematics and Optimization》1982,8(1):159-188
The Signorini problem for an elastic body admits a convenient formulation as a variational inequality. However, it is not coercive. In this note we establish a priori limitations for the solution, estimates of the contact set, and stability for the solution of this problem. The last section is devoted to the example of an infinite circular cylinder, in plane strain.This research was partially supported by the N. S. F. 相似文献
14.
交替方向法是求解可分离结构变分不等式问题的经典方法之一, 它将一个大型的变分不等式问题分解成若干个小规模的变分不等式问题进行迭代求解. 但每步迭代过程中求解的子问题仍然摆脱不了求解变分不等式子问题的瓶颈. 从数值计算上来说, 求解一个变分不等式并不是一件容易的事情.因此, 本文提出一种新的交替方向法, 每步迭代只需要求解一个变分不等式子问题和一个强单调的非线性方程组子问题. 相对变分不等式问题而言, 我们更容易、且有更多的有效算法求解一个非线性方程组问题. 在与经典的交替方向法相同的假设条件下, 我们证明了新算法的全局收敛性. 进一步的数值试验也验证了新算法的有效性. 相似文献
15.
A static contact problem for inhomogeneous elastic materials is studied with a non-polynomial growth of the elasticity under the Coulomb’s law of dry friction and the normal compliance condition. We demonstrate the results on existence and uniqueness of a solution to an abstract subdifferential inclusion and a variational–hemivariational inequality in the reflexive Orlicz–Sobolev space which are applied to the static elastic frictional problem. 相似文献
16.
Q. Z. Yang 《Journal of Optimization Theory and Applications》2006,130(3):547-549
Verma introduced a system of nonlinear variational inequalities and proposed projection methods to solve it. This system reduces to a variational inequality problem under certain conditions. So, at least in form, it can be regarded as a extension of a variational inequality problem. In this note, we show that solving this system coincides exactly with solving a variational inequality problem. Therefore, we conclude that it suffices to study the corresponding variational inequalities.This work was supported by the National Natural Science Foundation of China, Grant 10571134.Communicated by M. J. Balas 相似文献
17.
一个第二类变分不等式的有限元逼近 总被引:1,自引:0,他引:1
本短文讨论下述第二类变分不等式(见 [2, 4])的有限元逼近及其误差分析:其中是平面凸多边形区域的的边界, 且而 . 诸如热量控制问题,流体通过半可透性壁的扩散问题以及简化库仑摩擦接触问题的正则化方法等均可归为上述变分不等式(1)(见[2,3]).在文[2]中给出了上述变分不等式的有限元逼近格式,作出了收敛性分析及误差估计.本文的目的是进一步用数值积分简化上述有限元逼近格式并改进原有的估计误差. 设Th是的拟一致三角形部分,Vh是对应的线性元空间,且使得vh=0在上.[2]中用数值积分代替其中 Mi… 相似文献
18.
We consider the variational free boundary problem describing the contact of an elastic plate with a thin elastic obstacle. The contact domain is unknown a priori and should be determined. The problem is described by a variational inequality for a fourth-order operator. The constraint on the displacement is given on a set of dimension less than that of the solution domain. We find the boundary conditions on the set of the possible contact and their exact statement. We justify the mixed statement of the problem and analyze the limit cases corresponding to the unbounded increase of the elasticity coefficients of the contacting bodies. 相似文献
19.
Dynamical systems and variational inequalities 总被引:1,自引:0,他引:1
The variational inequality problem has been utilized to formulate and study a plethora of competitive equilibrium problems in different disciplines, ranging from oligopolistic market equilibrium problems to traffic network equilibrium problems. In this paper we consider for a given variational inequality a naturally related ordinary differential equation. The ordinary differential equations that arise are nonstandard because of discontinuities that appear in the dynamics. These discontinuities are due to the constraints associated with the feasible region of the variational inequality problem. The goals of the paper are two-fold. The first goal is to demonstrate that although non-standard, many of the important quantitative and qualitative properties of ordinary differential equations that hold under the standard conditions, such as Lipschitz continuity type conditions, apply here as well. This is important from the point of view of modeling, since it suggests (at least under some appropriate conditions) that these ordinary differential equations may serve as dynamical models. The second goal is to prove convergence for a class of numerical schemes designed to approximate solutions to a given variational inequality. This is done by exploiting the equivalence between the stationary points of the associated ordinary differential equation and the solutions of the variational inequality problem. It can be expected that the techniques described in this paper will be useful for more elaborate dynamical models, such as stochastic models, and that the connection between such dynamical models and the solutions to the variational inequalities will provide a deeper understanding of equilibrium problems. 相似文献
20.
In this work, a contact problem between an elastic body and a deformable obstacle is numerically studied. The bone remodeling of the material is also taken into account in the model and the contact is modeled using the normal compliance contact condition. The variational problem is written as a nonlinear variational equation for the displacement field, coupled with a first-order ordinary differential equation to describe the physiological process of bone remodeling. An existence and uniqueness result of weak solutions is stated. Then, fully discrete approximations are introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are obtained, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some 2D numerical results are presented to demonstrate the behavior of the solution. 相似文献